f(x) = a*x**3 + b*x**2 + c*x + d
f'(x) = 3*a*x**2 + 2*b*x + 1*c
f(0) = 0    # start at 0
f'(0) = 0   # want a flat slope
f(1) = 1    # end at 1
f'(1) = 0   # but flat at this end, as well.
solve: 
d = 0       # from f(0)
c = 0       # from f'(0)
b = 3, a=-2 # from f(1) and f'(1)